Advice needed – Double paying for auto insurance and GEICO refused to give a refund

I had GEICO as my first insurance and switched to Progressive before the second billing cycle began. I removed the payment method with GEICO and it was my fault for assuming that nonpayment would mean policy termination, but GEICO kept charging me and claim that I owe the months of payment before it was automatically cancelled because I did not submit my proof of residency which incidentally saved me from oweing more.
I have argued with GEICO's customer service back and forth, and they certainly could have done better in communicating that my policy was still active before but this doesn't matter at this point. GEICO stated they did not receive my written cancellation request (required by my state) so they refuse to backdate and remove the outstanding balance.
Now I'm getting text from Credit Collection Services I am worried that they will add a delinquent payment on my credit report. I am currently looking to file a complaint with my state's DOI and CFPB.

What should I do at this point? I saw online that there were incidents of such double paying but did not see how they resolve. I wonder if there's any legal basis for requesting a refund because GEICO's customer service will likely dismiss anything I request at this point.

Thank you for your advice in advance!!